Exponents Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
Which is larger, 343^4 or 434^3? Compute both to compare.

Solution

  1. 1
    Compute 34=3×3×3×3=813^4 = 3 \times 3 \times 3 \times 3 = 81.
  2. 2
    Compute 43=4×4×4=644^3 = 4 \times 4 \times 4 = 64.
  3. 3
    Compare: 81>6481 > 64, so 343^4 is larger.

Answer

34=81>43=643^4 = 81 > 4^3 = 64
A larger exponent does not always win. Here the base 3 raised to the 4th power beats the base 4 raised to the 3rd power because the extra multiplication round outweighs the larger base.

About Exponents

An operation representing repeated multiplication: ana^n means aa multiplied by itself nn times. For example, 23=2×2×2=82^3 = 2 \times 2 \times 2 = 8. Exponents extend to zero, negative, and fractional powers.

Learn more about Exponents →

More Exponents Examples

Example 1 easy

Compute [formula].

Example 2 medium

Simplify [formula].

Example 3 easy

Compute [formula].

Example 5 medium

Simplify [formula].

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